Which of the following statements about the $standarderror$ of the estimate is true?

• A. The $standarderror$ is not used when constructing confidence intervals.
• B. The $standarderror$ increases as the $samplesize$ increases.
• C. The $standarderror$ is always equal to the $populationstandarddeviation$.
• D. The $standarderror$ measures the variability of a $samplestatistic$, such as the $samplemean$, from sample to sample.

Answer: (D)

Verified step by step guidance

1. Understand that the standard error (SE) is a measure of the variability or dispersion of a sample statistic (like the sample mean) across different samples drawn from the same population.
2. Recall that the standard error is calculated as the population standard deviation (\sigma) divided by the square root of the sample size (n), expressed as: \[ SE = \frac{\sigma}{\sqrt{n}} \]
3. Recognize that as the sample size (n) increases, the denominator \( \sqrt{n} \) increases, which causes the standard error to decrease, meaning the estimate becomes more precise.
4. Note that the standard error is used in constructing confidence intervals to quantify the uncertainty around the sample statistic, so the statement that it is not used in confidence intervals is false.
5. Understand that the standard error is not equal to the population standard deviation; rather, it is derived from it and depends on the sample size, reflecting the variability of the sample statistic, not the population data itself.